The electrical power grid is experiencing important changes. First, introducing new power plants and enlarging the grid is becoming more expensive and complicated. Second, the introduction of more renewable power sources, which have a much higher output variance, will make it even harder to control and predict the state of the system. In this environment, a smart grid, where not only energy but also data is transmitted, appears to be a solution in the right direction as it gives further control to all parties involved in the various aspects of the power grid: generation, transmission, distribution, and consumption. Smart grids are the evolution of our current electrical grid and promise to solve many of the current limitations like managing sources with higher variability and increase security and reliability. But in order to use smart grids appropriately, new mechanisms and processes need to be put in place to control the flow of energy and achieve the promised goals. Demand shaping mechanisms are among the most crucial ones, since they allow the grid operators to control and shape the demand, reduce costs and peak to average consumption, as well as increase reliability and better control blackouts and brownouts.
The current smart grid approaches and related work may be organized generally into two main categories: demand response (DR) methods and grid/market modeling. Several different methods for demand response have been proposed in the literature. A good summary of the different DR approaches is presented in an article by M. Albadi and E. El-Saadany entitled “Demand response in electricity markets: An overview”, Power Engineering Society General Meeting (2007), pp. 1-5, IEEE, and in their follow up article entitled “A summary of demand response in electricity markets”, Electric Power Systems Research 78, No. 11 (November 2008), pp. 1989-1996. An additional, interesting source of DR approach results can be found in an article by J.-H. Kim and A. Shcherbakova entitled “Common failures of demand response”, Energy 36, No. 2 (February 2011), pp. 873-880, in which the authors list several implementations and trials done as well as the shortcomings they have observed, shedding light into which methods are better for controlling demand level.
The simplest approach of demand response methods is the direct control, which basically uses the ideas of dynamic demand implemented in Great Britain. An elaborate example of that approach appears in an article by G. Tejeda and A. Cipriano entitled “Direct Load Control of HVAC systems using Hybrid Model”, Predictive Control (2012), in which the authors control a HVAC (heating, ventilation and air conditioning) load directly. Their approach comes from the control theory perspective but, if the objective functions are changed for other economic quantities, a control system could be implemented that minimizes a desired metric, like generation cost or peak to average ratio (PAR), for electrical power grid purposes.
In terms of price/incentive based mechanisms, there are three main methods in demand response. The first one focuses on demand shedding as shown in an article by L. Chen, N. Li, S. H. Low and J. C. Doyle, entitled “Two Market Models for Demand Response in Power Networks”, Proceedings of First IEEE International Conference on Smart Grid Communications, (October 2010), pp. 397-402, IEEE. In this method, users will shed part of their demand, and the level of that shedding depends on the price offered by the generator or utility company. Thus, the results of the above-referenced article point towards how to compute the equilibrium prices such that a known amount d of demand can be shed. The authors consider that users shed demand linearly with prices, which could be true for small values of d but as d increases their model certainly will not work.
The second method is demand-source balancing. This method makes sure that the demand adapts to the current generation levels, something especially important in the presence of variable energy sources like wind or sun Several different methods are proposed in the literature (for example, in an article by A. D. Dominguez-Garcia and C. N. Hadjicostis entitled “Distributed algorithms for control of demand response and distributed energy resources”, Proceedings of the 50th IEEE Conference on Decision and Control (December 2011), pp. 27-32; in an article by P. Loiseau, G. Schwartz, J. Musacchio, S. Amin, and S. Sastry, entitled “Congestion pricing using a raffle-based scheme”, Proc. of International Conference on Network Games, Control and Optimization, No. 2, (2011) pp. 1-8; in an article by A.-H. Mohsenian-Rad, V. W. S. Wong, J. Jatskevich, R. Schober, and A. Leon-Garcia, entitled “Autonomous Demand-Side Management Based on Game-Theoretic Energy Consumption Scheduling for the Future Smart Grid”, IEEE Transactions on Smart Grid 1, No. 3 (December 2010), pp. 320-331; and in an article by F. Partovl, M. Nikzad, B. Mozafari, and A. M. Ranjbar, entitled “A stochastic security approach to energy and spinning reserve scheduling considering demand response program”, Energy 36, No. 5 (May 2011), pp. 3130-3137). One of the most interesting methods is the one proposed by the Mohsenian-Rad, et al. article above since the authors arrive to a distributed method that can balance the demand level given the generation output with the objective of minimizing the generation cost.
The third main demand response method is demand shifting. This is the one most directly related to the problem of demand shaping since in this case the users agree to shift their loads in time, according to a price signal by the utility company. An example of such an approach appears in an article by M. Kraning, E. Chu, J. Lavaei, and S. Boyd, entitled “Message Passing for Dynamic Network Energy Management” (2012) in which users give their preferences and restrictions for their different appliances (like washing machines, electric vehicles, etc.) and then, through a distributed algorithm, the demand level is defined to achieve a certain control objective. The main issue with this method is that it is not truthful (i.e. the users can cheat the system by not revealing their true requirements and thus obtain benefits above the social optimum). Also, there are some privacy concerns in terms of the information the users must share. Still, it is a very interesting approach to see how loads can be shifted around.
More related to the methodology side, one article (by W. Chen, D. Huang, A. A. Kulkarni, J. Unnikrishnan, Q. Zhu, P. Mehta, S. Meyn, and A. Wierman entitled “Approximate dynamic programming using fluid and diffusion approximations with applications to power management”, Proceedings of the 48th IEEE Conference on Decision and Control (CDC), (December 2009), pp. 3575-3580) discusses one methodology that can be used to compute optimal solutions of complex models. This method could be interesting if there is a need to find an equilibrium point or a price value, and, especially, if there is a focus on using stochastic models to represent a system.
The literature also discusses how to model the power grid and more importantly, how to model or find solutions for the market that works over the grid. It is important to remember that this market basically works in three levels: a long-term market, day-ahead market, and real time market. In the long term market generators and large consumers or utility companies sign agreements for power delivery many weeks, months, or even years ahead. Then in the day-ahead market utility companies purchase whatever additional energy they might need given the much better forecasts they have for the next day, as well as the reserve required. The third market is the real time market or spot market, which is between 5 to 10 minutes ahead of the actual real-time demand and it is used to match the demand exactly.
In one article, the authors highlight the difficulties the future grid will have, which is important since some of the new metrics a future smart grid might be of interest while solving current issues with demand shaping (see the article by M. Negrete-Pincetic and S. Meyn, entitled “Intelligence by Design for the Entropic Grid”, “Intelligence by Design for the Entropic Grid”, Power and Energy Society General Meeting, 2011. pp. 1-8, IEEE). One of the most interesting and useful models for the energy market is the one developed in a document by I-K. Cho and S. P. Meyn, entitled “Efficiency and marginal cost pricing in dynamic competitive markets with friction”, Theoretical Economics 5, No. 2 (2010), pp. 215-239 in which the authors formulate the general model and are able to compute equilibrium points given certain simplifications. The main takeaway of this document is that, by adding friction to the market model (which appears due to the ramp-up constraints given by generators), it is now possible to achieve solutions with price volatility similar to the ones observed in real energy markets. This is a key point since the first step in most other papers in the area is to simplify the model by eliminating ramp-up requirements, and thus those results could be far off from reality. In follow-up papers, the respective authors further analyze their models with additional components, such as variable energy sources (see the papers by S. Meyn, M. Negrete-Pincetic, G. Wang, A. Kowli, and E. Shafieepoorfard entitled “The value of volatile resources in electricity markets”, 49th IEEE Conference on Decision and Control (CDC), (December 2010), pp. 1029-1036; by G. Wang, A. Kowli, M. Negrete-Pincetic, E. Shafieepoorfard and S. Meyn entitled “A Control Theorist's Perspective on Dynamic Competitive Equilibria in Electricity Markets”, Proceedings of the 18th IFAC World Congress (2011), pp. 4933-4938; and by G. Wang, M. Negrete-Pincetic, A. Kowli, E. Shafieepoorfard, S. Meyn, and U. V. Shanbhag, entitled “Dynamic Competitive Equilibria in Electricity Markets”, Control and Optimization Methods for Electric Smart Grids, Volume 3, 2012, pp 35-62). These are very interesting results since they are able to model the system considering that both demand and generation of energy are stochastic processes, which is useful for other approaches. Another article analyzes the system in terms of its reliability, which is something that might also be of interest (see the article by M. Chen, I-K. Cho, and S. P. Meyn, entitled “Reliability by design in distributed power transmission networks”, Automatica 42, No. 8 (August 2006), pp. 1267-1281).
Another approach for modeling this market is given in an article by S. Worgin, B. F. Hobbs, D. Ralph, E. Centeno, and J. Barquin, entitled “Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition”, Mathematical Programming, September 2013, Volume 140, Issue 2, pp 295-322, in which the authors not only analyze the perfect competition setting but also the oligopolistic one in which energy producers are not price takers as in most of the rest of the literature.
Finally, how to add variable sources to the energy market model can be found in an article by J. Nair, S. Adlakha, and A. Wierman, entitled “Energy Procurement Strategies in the Presence of Intermittent Sources”, 2012. The most interesting result in this article is how they are able to compute procurement strategies when the energy sources have high variability while at the same time being able to model the three levels of the energy market. They do it by adding error to the forecasts for each of the different markets which could be useful for other forecasting methodologies.